Two-pole channel-dropping filter



April 29, 1969 R. D. STANDLEY TWO-POLE CHANNEL-DROPPING FILTER Sheet Filed Sept. 7, 1967 Eu 5 @562 XE y? E m 0 RD W m A mmJ 1 E WW \KQQQ April 29, 1969 R. 0. STANDLEYY: 3,44 7

TWO -POLE CHANNEL-DROPPING FILTER Filed Sept. 7, 1967 Sheet 3 of 2 FIG. 2 PROTOTYPE NETWORK FOR A TWO-POLE CHANNEL ORORR/NO FILTER United States Patent O1 fice 3,441,878 Patented Apr. 29, 1969 US. Cl. 333-6 4 Claims ABSTRACT OF THE DISCLOSURE Channel-dropping filters having steeper skirt selectivity are realized in an arrangement that includes a twostage band-rejection filter and a multiple-resonant branching filter. The latter comprises a resonant section of dualmode circular waveguide that is supportive of both the TE and TE circular electric modes over the band of frequencies occupied by the channel to be dropped, and is resonant for the TE mode. A second resonator, comprising a section of rectangular waveguide, is wrapped around the dual-mode resonator such that one of the wide walls of the rectangular guide and a portion of the wall of the circular guide are shared in common.

Coupling between the two resonators is provided by means of a multiplicity of apertures uniformly distributed about the portion of common wall. Coupling out of the second resonator is through an aperture located in the other wide wall.

BACKGROUND OF THE INVENTION The TE circular-electric mode of wave propagation in round waveguides has received considerable attention due to its recognized low-loss propagation characteristic. The problem of multiplexing in a communication system using this mode of wave propagation was first considered by E. A. J. Marcatili in his article entitled Mode- Conversion Filters, published in the January 1961 issue of the Bell System Technical Journal, pages 149-184. The filter described by Marcatili in this article, and in his United States Patent 2,950,452, uses TE to TE circular-electric mode-conversion resonators to achieve channel separation.

In United States Patent 2,963,663, also issued to E. A. J. Marcatili, there is described a second type of channel-dropping filter for use with the TE mode of wave propagation.

Both these classes of filters have single-pole, maximally-fiat frequency response characteristics which places a limit upon the number of channels which can be included Within a given frequency band. As the bit rate, proposed to be used in pulse code modulation systems currently under study, is increased, implying an increased bandwidth per channel, multiple-pole filters are necessary in order to realize more efficient use of the available bandwidth. In particular, because of the steeper skirt selectivity, characteristic of the frequency response of a multi-pole filter, the channel bandwidth can be increased without increasing the 'channel-to-channel separation or, alternatively, the channel-to-channel separation can be decreased for a given channel bandwidth, thus increasing the total number of permissible channels.

SUMMARY OF THE INVENTION A channel-dropping filter, in accordance with the present invention, includes a two-stage band-rejection filter and a multiple-resonant branching filter. The latter comprises a resonant section of dual-mode circular waveguide that is suportive of both the TE and TE circular electric modes over the band of frequencies occupied by the channel to be dropped, and is resonant for the TE mode. A second resonator, comprising a section of rectangular Waveguide, is wrapped around the dual-mode resonator such that one of the wide walls of the rectangular guide is common to a portion of the wall of the circular guide.

Coupling between the two resonators is provided by means of a multiplicity of apertures uniformly distributed about the portion of common wall. Coupling out of the second resonator is through an aperature located in the other wide wall. In one illustrative embodiment of the invention to be described in greater detail hereinbelow, the dropped channel is coupled into a rectangular waveguide, one end of which abuts upon the second resonator to form an E-plane T-junction.

In operation, the input signal, comprising a plurality of channels propagating in the TE circular electric mode, is coupled into one end of the resonant section of dual-mode waveguide. The latter, along with the two band-rejection filters coupled to the other end of the branching filter, cause the channel that is to be dropped to be coupled through the branching filter to the output rectangular waveguide.

It is an advantage of the present invention that by virtue of the arrangement of resonant sections in the branching filter, a two-pole, maximally-flat frequency response is obtained.

These and other objects and advantages, the nature of the present invention, and its various features, will appear more fully upon consideration of the various illustrative embodiments now to be described in detail in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a two-pole channel-dropping filter in accordance with the invention;

FIG. 2, included for purposes of explanation, shows a prototype network for the filter of FIG. 1; and

FIGS. 3 and 4 illustrate alternate arrangements for coupling wave energy out of the channel-dropping filter of FIG. 1.

DETAILED DESCRIPTION Referring to the drawings, FIG. 1 shows a two-pole, channel-dropping filter in accordance with the invention, comprising a multiple-resonant branching filter 10, and a two-stage, band-rejection filter 11 longitudinally disposed along circular waveguide 9. The latter is proportioned to support the lowest order circular electric mode, i.e., the TE mode, over a band of frequencies including f f f,,, and to be non-supportive of any of the higher order circular electric modes over this frequency band.

For purposes of illustration, the band-rejection filter is of the type described in United States Patent No. 2,950,452, issued to E. A. J. Marcatili on Aug. 23, 1960, and comprises a pair of dual-mode resonators 12 and 13. The design and mode of operation of this filter is described in detail in the above-mentioned Marcatili patent. Briefly, each resonator is proportioned to support wave energy over a band of frequencies centered at f, in both the TE and TE circular electric modes and, in addition, to be resonant at frequency f, for the TE mode. The electrical center-to-ceuter spacing between resonators 12 and 13 is equal to an odd multiple of 1r/Z radians with respect to the center frequency of the channel to be rejected. The equivalent physical center-to-center spacing can be calculated using equations 107 and 108, found on page of the above-identified article by Marcatili.

Branching filter 10 similarly comprises a dual-mode resonator 14, proportioned to resonate the TEgg mode at center frequency 73. In addition, there is a resonant section of conductively-bounded rectangular Waveguide 15 wrapped around the circumference of resonator 14 such that the wide walls of the wrap-around guide are parallel to the longitudinal axis of Waveguide 9. In the illustrative embodiment of FIG. 1, a portion 16 of the circumferential surface of resonator 14 is shared in common with, and forms one of the wide walls of resonant guide 15.

Coupling between resonator 14 and waveguide 15 is through a plurality of apertures 17 extending through the common wall portion 16. The apertures are uniformly spaced about the circumference of resonator It with a center-to-center spacing between adjacent apertures equal to one guide wavelength of the wave energy in guide 15. As is known, the guide Wavelength of the wave energy in guide 15 is a function of the width of guide 15.

A typical number of coupling apertures between resonators 14 and 15 is about six. As the number of apertures is increased, the bandwidth of the branching filter tends to decrease. This consideration sets an upper limit to the number of apertures. As the number of apertures is decreased, on the other hand, the tendency for mode conversion to occur in the circular waveguide between the TE mode and other non-circular modes, is increased. This consideration sets a lower limit to the number of apertures that are used.

Coupling out of the branching filter, to output waveguide 19, is through an aperture 18 in the outer wide wall 20 of guide 15. The location of this aperture depends upon the nature of the output coupling. In the embodiment of FIG. 1, output waveguide 19 is a conductively-bounded rectangular waveguide oriented with its wide walls parallel to the longitudinal axis of guide 9, and with one end abutting upon the outer wall 20 of guide 15 to form an E-plane T-junction. In this arrangement, aperture 18 is symmetrically located between any pair of adjacent apertures 17.

The electrical center-to-center spacing between branching filter and the adjacent band-rejection filter 12 is equal to an odd multiple of 7r/2 radians at the center frequency f of the channel to be dropped.

In operation, wave energy, including a plurality of channels centered at frequencies f f f propagating along waveguide 9 in the TE mode, is coupled into port 1 of the channel-dropping filter comprising branching filter 10 and band-rejection filter 11. Wave energy centered at frequency f,, for which the filter is designed, is separated from the rest of the channels and leaves by way of port 2 in output Waveguide 19. The remaining channels f f f f i continue propagating along waveguide 9 in the TE mode to a next channel separating filter by way of port 3.

Some insight into the electrical behavior of the channel-separating filter of FIG. 1 can be obtained by considering the prototype network shown in FIG. 2. The prototype network consists of complementary admittances connected in shunt. The elements of the network have been chosen to yield a two-pole, maximally-fiat insertion loss response between ports 1 and 2 while maintaining a constant input admittance as a function of frequency. (See G. L. Matthaei et al., Design of Microwave Filters, Impedance Matching Networks, and Coupling Structures, McGraw-Hill Book Company, Inc., New York, 1964, and G. L. Matthaei et al., Novel Microwave Filter Design Techniques, Contact DA 36039-AMC-00084(E), Final Report, Chapter 10, Stanford Research Institute, Menlo Park, Calif, December 1964.)

Total power transfer occurs at zero frequency, and half-power transfer occurs at an input angular frequency of one radian. The prototype network is converted to a network having total power transfer at some frequency w through use of the angular frequency mapping function where w=angular frequency variable of the prototype network w=angular frequency variable of the desired network QL= o 1 2 m w half-power angular frequencies of the desired network.

The relationship between the prototype network param eters and the parameters of the structure shown in FIG. 1 are discussed in detail hereinbelow. For the purpose of obtaining a qualitative understanding of electrical behavior it is sufficient to state that the performance of the microwave structure is identical to that of the frequency mapped prototype network subject only to the approximations involved in relating their respective parameters.

DESIGN PROCEDURE The necessary equations for designing a channel dropping filter in accordance with the invention are given below under the heading Derivation of the Design Equations. While much detail is included therein, it is sulficient merely to use the results thus obtained and design the various elements in "accordance with the following procedure.

(1) Equations 2, 15 and 16 are used to compute the external Qs of the mode conversion resonators 12, 13 and 14. 1

(2) The wrap-around resonator, formed by waveguide 15, is designed using Equations 1 and 7. The additional feature that the coupling apertures 17 are to be separated by one guide wavelength in the wrapped structure at resonance must also be observed. As noted above, this is controlled primarily by the width, a of waveguide 15, and also by the diameter of resonator 14. The thickness of wall 16 in which apertures 17 are located is also significant.

(3) The coupling aperture dimensions are determined by Equations 2 and 14-.

(4) The magnitude of the normalized coupling reactance required at the output aperture 18 (X /R is determined from Equation 6.

Derivation of the design equations A. BRANCHING FILTER The branching filter consists of a TE TE mode conversion resonator 14 coupled to a wrapped rectangular waveguide resonator 15. The physical parameters of the latter are to be related to that portion of the network of FIG. 2 consisting of the elements g g and g The parameters of interest are the external Qs, Q,,, of the two resonators and the coefficient of coupling between them, k Using the notation of Chapter 8 of the above-cited book by Matthaei, there is obtained Qew= 0 1 1 QL'= 1 QL Qem 2 0 1 QL l QL 12=1 w1'Q1.\ E;=1/ 1'QL where m is the bandpass edge angular frequency of the proto type network, and

Q;, is the desired loaded Q of the diplexer.

The subscripts wand m refer to the wrapped resonator and the mode conversion resonator, respectively.

The next step is to derive the expressions for the external Qs and coupling coefiicient in terms of the physical parameters of the structure.

The results of Marcatilisanalysis given in his abovecited article show that 'Qem'=QL where i c j Q is given by Marcatilis equation '(70).

The external Q of the wrapped resonator; Q is obtained from the defining equation 2 am m QBW I R where wq=21rx resonant frequency: X =resonator reactance function; and R =coupled resistance.

Z ==characteristic impedance of the wrapped guide;

Ag =guide wavelength of the wrapped guide at resonance;

X =reactance of aperture 18;

R =characteristic impedance of the input guide;

and K 0 1ength ofthe wrapped structure in radians at resonance.

In general 0 :1rp where is the number of coupling apertures. For loose coupling is the power coupling coefficient between guides.

The coupling coefficient k is given in terms of the resonator parameters by where X =c0upling reactance;

and

=slope parameter of the first resonator; 0J0

=slope parameter of the second resonator. W0

2 II HI 12 where Z is the characteristic impedance of the TE waveguide.

- If loose coupling is assumed,.Bethe.s small hole coupling theory can be applied to yield 2 ab R A 0 a=wrapped guide width;

b= wrapped guide height;

p=number of apertures;

R=radius of TE guide;

A =TE guide wavelength; A =wrapped guide wavelength;

and

M=magnetic polarizability of the aperture.

The above assumes the apertures to be A apart in the wrapped structure. The magnetic polarizability of the aperture is determined from,

. where M =static polarizability of the aperture;

A =cutotf wavelength of the dominant aperture mode; t=aperture thickness;

and

A=empirical constant.

Matthaeis book contains an excellent collection of data on M for various types of apertures.

The above analysis when rearranged yields The latter then represents the relationship between the required aperture dimensions and the characteristics of the filter.

B. REJECTION FILTERS From Matthaei it is found that the loaded Q5 of the rejection filters are given by where Q applies to the rejection filter nearest the branching filter. The loaded Qs of the rejection filters in terms of the physical parameters are given in Marcatilis article by Equation 139.

In the illustrative embodiment of a two-pole channeldropping filter described in connection with FIG. 1, resonant, dual-mode, band-rejection filters are shown. It will be recognized, however, that other filter arrangements can just as readily be used. As an example of one such other filter, employing resonant irises, see United States Patent 2,991,431, issued to S. E. Miller. July 4, 1961. In addition, alternate arrangements for coupling out of wraparound waveguide 15 can be used, as illustrated in FIGS. 3 and 4. For example, in FIG. 3, a rectangular output waveguide 30 is oriented at a tangent to wrap-around waveguide 15, with the narrow walls of the two guides parallel to each other. Coupling is through an aperture 31 which extends through one of the wide walls of each of the respective guides at their region of contact. A conductive, shorting plunger terminates one end of guide 30 approximately one-half wavelength away from aperture 31. The dropped channel is extracted from the other end of guide 30. As in the embodiment of FIG. 1, output aperture 31 is symmetrically located between any pair of apertures 17.

In the arrangement illustrated in FIG. 4, a coaxial cable 40 abuts upon the outer wide wall of waveguide 15. A probe 42, constituting an extension of the center conductor of coax 40, extends into waveguide through an aperture 41. In this coupling arrangement, aperture 41 is asymmetrically located with respect to any pair of adjacent apertures 17. More particularly, aperture 41 is spaced away from the next adjacent aperture 17 a distance equivalent to an odd multiple of a quarter of a wavelength at frequency 71.

Thus, in all cases it is understood that the abovedescribed arrangements are illustrative of a small number of the many possible specific embodiments which can represent applications of the principles of the invention. Numerous and varied other arrangements can readily be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention.

I claim:

1. In an electromagnetic wave transmission system supportive of wave energy in the TE circular electric mode of propagation over a frequency range f through f and nonsupportive of said wave energy in the higher circular modes, a channeldropping filter for extracting a band of Wave energy centered at a frequency 1, within said range of frequencies;

said filter including a branching filter and a two-stage band-rejection filter spaced apart along said system at intervals equal to an odd multiple of 1r/Z radians at frequency f characterized in that said branching filter comprises;

a multimode section of circular waveguide proportioned to support both the TE and TE circular electric modes of propagation at said frequency f, and to resonate said TE circular electric mode; an annular section of rectangular waveguide wrapped about the outer circumference of said multimode section of circular waveguide and adapted to resonate at frequency f means for coupling between said rectangular Waveguide and said circular waveguide comprising a multiplicity of apertures uniformly distributed about the circumference of said circular waveguide at intervals equal to one guide wavelength of said rectangular waveguide and extending from within said circular waveguide to Within said rectangular waveguide through one of the wide walls thereof;

and means for extracting wave energy at frequency f from said rectangular waveguide.

2. The filter according to claim 1 wherein said means for extracting wave energy from said rectangular waveguide comprises an aperture located in the other wide wall of said rectangular waveguide symmetrically situated between any adjacent pair of said multiplicity of apertures.

3. The filter according to claim 1 wherein said bandrejection filter comprises two dual-mode resonant sections of circular waveguide proportioned to support both the TE and TE circular electric modes of propagation at frequency f and to resonate said TE circular electric mode.

4. The filter according to claim 1 wherein said means for extracting wave energy from said rectangular waveguide comprises an aperture located in the other wide wall of said rectangular waveguide spaced an odd multiple of a quarter of a guide wavelength from any adjacent pair of said multiplicity of apertures.

References Cited UNITED STATES PATENTS 8/1960 Marcatili. 12/1960 Marcatili 3339 US. Cl. X.R. 333-73 

